This invention relates to modulation methods for wireless signal transmission. More particularly, the invention relates to modulation methods useful in fading environments in conjunction with multiple-antenna arrays.
It is generally desirable to reduce error rates, and to increase transmission rates, in wireless transmission systems. Multiple-antenna arrays can be used to achieve these desirable effects.
Fading is one of several physical phenomena that tend to increase error rates, or to reduce channel capacity, in traditional single-antenna wireless transmission systems. Fading is the result of destructive interference, at the receiver, between correlated signal portions that because of scattering have arrived over different-length paths.
In fading environments, the capacity of a multiple-antenna communication link may increase with the size of the transmitter or receiver array. This effect has been predicted, e.g., for rich scattering environments in which fading is xe2x80x9cflat.xe2x80x9d In flat fading, the propagation coefficients that describe the effect of the physical transmission channel on the transmitted signal are approximately independent of frequency over the signal bandwidth. Flat fading can be achieved in practice for a particular environment if the bandwidth is not too great, or if it is restricted appropriately.
Some methods for exploiting such an increase in capacity use knowledge of the propagation coefficients between all pairs of transmitter and receiver antennas. Such knowledge is gained, e.g., by training the receiver with known training signals from the transmitter.
Communication methods that use such a training procedure are described, for example, in the co-pending U.S. patent application Ser. No. 08/938,168, commonly assigned herewith, filed on Sep. 26, 1997 by B. M. Hochwald et al. under the title, xe2x80x9cMultiple Antenna Communication System and Method Thereof.xe2x80x9d
Other co-pending patent applications, commonly assigned herewith, that describe related subject matter are Ser. No. 08/673,981, filed on Jul. 1, 1996 by G. J. Foschini under the title xe2x80x9cWireless Communications System Having a Layered Space-Time Architecture Employing Multi-Element Antennas,xe2x80x9d Ser. No. 09/060,657, filed on Apr. 15, 1998 by G. J. Foschini and G. D. Golden under the title xe2x80x9cWireless Communications System Having a Space-Time Architecture Employing Multi-Element Antennas at Both the Transmitter and Receiver,xe2x80x9d and Ser. No. 09/112853, filed on Jul. 10, 1998 by T. L. Marzetta under the title xe2x80x9cDetermining Channel Characteristics in a Space-Time Architecture Wireless Communication System Having Multi-Element Antennas.xe2x80x9d
Unfortunately, training intervals cut into the available time during which data may be transmitted. The length of this interval increases as the number of transmitter antennas is increased. Moreover, the propagation coefficients can be treated as constant only over an average period of time referred to as the fading coherence interval. To be effective, training should be repeated at least once per such interval. However, fading is very rapid in some environments, such as those in which a mobile station is operating within a rapidly moving vehicle. For rapid fading environments, the time between fades may be too short for the communication system to learn the propagation coefficients belonging to even one transmitting antenna, much less those of a multiple-antenna array.
Thus, there are advantages to a signal modulation method that can at least partially realize the theoretical benefits of multiple-antenna arrays in fading environments without the benefit of known propagation coefficients.
In the co-pending U.S. patent application Ser. No. 09/134,297, commonly assigned herewith, filed on Aug. 14, 1998 by B. M. Hochwald et al. under the title, xe2x80x9cWireless Transmission Method for Antenna Arrays, Having Improved Resistance to Fading,xe2x80x9d there was described a new method of signal modulation. This new method, which we refer to as xe2x80x9cUnitary Space-Time Modulation (USTM),xe2x80x9d is robust against fading and receiver-induced noise in flat fading environments. Significantly, it does not require knowledge of the propagation coefficients, although in some implementations, such knowledge can be used to further improve performance.
In USTM, each message to be transmitted is transformed into a sequence of signals selected from a constellation of L possible signals, L a positive integer. (Thus, each transmitted signal embodies a number of bits given by log L. In the present discussion, xe2x80x9clogxe2x80x9d will denote the binary logarithm.) Each of these signals is, itself, a time sequence of complex amplitudes for transmission by the transmitting antenna or antennas. The term xe2x80x9ccomplexxe2x80x9d includes pure real and pure imaginary values. (We will speak, in general terms, of a transmitting array having a plurality of transmitting antennas. However, it should be noted that the number M of transmitting antennas may be 1.) The transmissions by all of the antennas in the transmitting array are concerted. All of these transmissions (for a given signal) are made in the same sequence of T successive time units (which we refer to as symbol intervals), T a positive integer.
Thus, a signal may be represented by a complex-valued matrix having T rows and M columns. The term xe2x80x9ccomplex-valuedxe2x80x9d matrix includes matrices some or all of whose elements are pure real or pure imaginary. Each column corresponds to a respective antenna of the transmitting array, and represents the sequence of baseband-level complex amplitudes to be transmitted by that antenna. Each row corresponds to a particular one of the T symbol intervals, and describes the complex amplitude to be transmitted by each respective antenna during that interval. Such a set of complex amplitudes is referred to as a xe2x80x9csymbol.xe2x80x9d Each symbol is distributed in space (i.e., across the transmitting array), and each signal is composed of T symbols distributed in time.
Because each signal is distributed in space and time, and because each signal matrix has orthonormal columns, we refer to the signal matrices as unitary space-time signals.
For data transmission rates to be advantageously high, it is desirable in many cases to have very large constellations of unitary space-time signals, exemplarily constellations of hundreds of thousands of signals, or even more. The likelihood of misidentifying a received unitary space-time signal is minimized if for each pair of non-identical signal matrices, each column of one is orthogonal to every column of the other. However, elementary principles of matrix algebra dictate that over the entire constellation, there can be no more than T mutually orthogonal columns. Many practical constellations will be much larger than T, thus precluding such pairwise column orthogonality for most of the signals. In such cases, the likelihood of receiver error is advantageously reduced by constellations in which there are relatively low correlations between pairs of signal matrices.
Because signal constellations may be very large, naxc3xafve efforts to construct appropriate constellations will generally be very demanding of computational resources. One solution to this problem is described in the co-pending U.S. patent application Ser. No. 09/206843, commonly assigned herewith, filed on Dec. 7, 1998 by B. M. Hochwald et al. under the title, xe2x80x9cWireless Transmission Method For Antenna Arrays Using Unitary Space-Time Signals.xe2x80x9d Described there is a method for generating a signal constellation from an initial Txc3x97M signal matrix and a generator matrix which is Txc3x97T unitary. The product obtained by left multiplying the initial signal matrix by the generator matrix is a further signal matrix. Left-multiplying the product by the generator matrix yields yet a further signal matrix, and so on for further repeated applications of the generator matrix. Significantly, the generator matrix can be tailored in such a way that the resulting product matrices tend to have relatively low correlations with each other. Thus, an appropriate subset of these product matrices is advantageously employed as a signal constellation.
Although such an approach as that described above is useful, there remains a need for still higher data transmission rates using multiple-antenna arrays.
We have discovered a method for generating unitary space-time signals belonging to constellations of arbitrary size. Our generation method is of low computational complexity. The resulting unitary space-time signals have statistical properties that are favorable for reliable use in communication, and they can lead to very high data transmission rates.
In a broad aspect, our new generation method involves the mapping of binary strings of data to matrix products of a particular kind. Each matrix product is obtained by left-multiplying an initial Txc3x97M matrix by an ordered multiplicative sequence of at least two, but not more than RT, Txc3x97T unitary matrices, which we also refer to herein as complex rotation matrices. RT is a positive integer to be discussed below. The result is a unitary space-time signal matrix that may be transmitted.
An ordered set of Txc3x97T unitary matrices is provided. These are referred to as the generator matrices. Each generator matrix corresponds to a single bit or a collection of bits of a binary string that is to be mapped. Each generator matrix is raised to a power equal to an integer exponent. The value of the exponent is determined by the pertinent bit or collection of bits. A generator matrix raised to the zero power is defined to be an identity matrix. The exponentiated matrices, in their assigned sequential order, then left-multiply the initial Txc3x97M matrix.
In an exemplary embodiment of the invention, there are RT generator matrices. The ordinal position of each generator matrix corresponds to the ordinal position of a corresponding bit in the binary strings that are to be mapped. The mapping of a binary string is achieved by assigning as the exponent for each generator matrix the value of its corresponding bit (or, alternatively, the complementary value of the corresponding bit). Equivalently, each generator matrix whose corresponding bit is, e.g., a 1 bit is retained, and each generator matrix whose corresponding bit is a 0 bit is replaced by an identity matrix.
In alternate embodiments of the invention, the choice between a given generator matrix and an identity matrix may be responsive to a higher-level property of the string then raw bit values. For example, it may be responsive to transitions between bits. Alternatively, such choice may be responsive, in effect, to a secondary string of bits obtained from the original string by coding, encryption, or data compression.
It will be appreciated that the signal matrices generated as described above belong to a constellation of size L=2RT. The parameter R is the data transmission rate in bits per symbol interval. Transmission of a complete signal matrix requires T symbol intervals, one for each row of the signal matrix.